摘 要
本論文係採用彈塑性大變形-大應變理論及updated Lagrangian formulation(ULF)，配合增量原理與CST(constant strain triangular)元素理論，建立一套有限元素分析模式，藉以分析軸對稱性金屬在冷擠製程中之變形及受力狀況。
由於金屬成形的過程中，元素主軸具有旋轉的現象，故本論文以Jaumann rate of Euler stress做為材料構成方程式中的應力變化率，並導出適當之幾何剛性矩陣。同時，亦考慮工件變形時的幾何非線性，而推導出在材料與模具接觸面上所衍生的荷重修正矩陣與摩擦修正矩陣，再將上述三項剛性矩陣偶合入有限元素法中的彈塑性剛性方程式，而合理的推導出材料之統制方程式。並依據此統制方程式發展出一套電腦軟體模擬程式，以其分析模擬金屬擠製成形製程的全部變形履歷資料，如塑性區的進展、加工時所需施加的加工力、工件成形之應力分佈、節點之力與位移關係、工件對模具之側向壓力及加工後成品之形狀等，最後並輔以實際的冷擠實驗來驗證，並由模擬所得的資料計算出模具所承受的側向壓力，俾供在冷擠製程及模具設計中尋求最佳的外形尺寸之參考。

ABSTRACT
This study adopts elasto-plastic large deformation-large strain theory and updated Lagragian formulation (ULF) to harmony with incremental theory as well as constant strain triangular (CST) element to create a FEM analysis code in order to analyze cold extrusion process.
Due to the process of metal forming, principal axis has a revolving phenomenon, the based on Jaumann rate of Euler stress was adopt as stress variation rate of material constitutive equation, a geometric matrix will be led into governing equation. Meanwhile, geometric nonlinearity of work-piece deformation will be considered and derivative load correction matrix and friction correction matrix of material of contact surface will also be introduced. The above-mentioned three stiffness matrices are coincidentally to FEM elasto-plastic governing equation. According to the governing equation to develop analysis code and applied it to cold extrusion process, The entire deformation data, such as progress of plasticity, processing force, stress distribution of work-piece under deformation, nodal force, lateral pressure of die and shape of finished products after unloading will be gained, The numerical simulation results will be comparing with the experimental results, and it proved that the simulated results kept reasonable agreement with the experiment. This work has provided an improved understanding of the cold extrusion process for improving the manufacturing processes and the design of tools.

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